Stochastic Models of Lunar Rocks and Regolith. Part I. Catastrophic Splitting Theory

摘要

It is assumed that a rock on the lunar surface loses mass as a result of the random bombardment by meteoroids. The mass of rock can be modelled as a non-increasing stochastic process with independent increments. In some cases, Filippov's model of a self-similar independent splitting process can be solved exactly. These results are extended in two directions. A new explicit asymptotic number density, which depends on a confluent hypergeometric function of the second kind, is obtained for the case that the one-shot splitting law is a two-term polynomial. The average number density with respect to a distribution of initial rock masses and initial rock birthdays has also been studied. The appropriate model parameters are estimated from laboratory hypervelocity impact and possible rock-size distributions (all approximately inverse power laws) derived for young rock populations, old rock populations, and mixtures of rock populations of various ages. (Author)